Department of Physics, Yeshiva University, New York, New York 10016, USA.
Department of Physics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
Nat Commun. 2017 Feb 23;8:14587. doi: 10.1038/ncomms14587.
Mechanical systems can display topological characteristics similar to that of topological insulators. Here we report a large class of topological mechanical systems related to the BDI symmetry class. These are self-assembled chains of rigid bodies with an inversion centre and no reflection planes. The particle-hole symmetry characteristic to the BDI symmetry class stems from the distinct behaviour of the translational and rotational degrees of freedom under inversion. This and other generic properties led us to the remarkable conclusion that, by adjusting the gyration radius of the bodies, one can always simultaneously open a gap in the phonon spectrum, lock-in all the characteristic symmetries and generate a non-trivial topological invariant. The particle-hole symmetry occurs around a finite frequency, and hence we can witness a dynamical topological Majorana edge mode. Contrasting a floppy mode occurring at zero frequency, a dynamical edge mode can absorb and store mechanical energy, potentially opening new applications of topological mechanics.
机械系统可以表现出与拓扑绝缘体相似的拓扑特征。在这里，我们报告了一大类与 BDI 对称类相关的拓扑力学系统。这些系统是由具有中心反演但没有镜面的刚体自组装链组成的。BDI 对称类的粒子-空穴对称性特征源于平移和旋转自由度在反演下的不同行为。这一特性以及其他一些普遍性质使我们得出了一个显著的结论，即通过调整物体的回转半径，我们总是可以同时在声子谱中打开一个间隙，锁定所有特征对称性，并产生一个非平凡的拓扑不变量。粒子-空穴对称性发生在有限的频率附近，因此我们可以观察到动力学拓扑马约拉纳边缘模式。与发生在零频率的柔体模式相反，动力学边缘模式可以吸收和储存机械能，为拓扑力学的新应用开辟了可能性。
